Gradient coils constitute a major piece of hardware in modern Magnetic Resonance Imaging (MM) scanners. Gradient coils are particularly important in studies which explore brain structural connectivity, due to the fact that an insufficient magnetic field strength generated by a gradient coil may limit the imaging resolution and sensitivity that may be achievable in the MM scanners. Thus, the magnetic field strength and slew rate (i.e., the speed of the coil switching) of a gradient coil have been important elements in evaluating the capacity of MRI scanners.
The performance of the gradient coil is one of the primary limiting factors in high speed, high resolution magnetic resonance imaging (MRI), and in diffusion MRI. There has been a consistent drive for higher magnetic field strength to achieve higher signal-to-noise ratio and stronger magnetic susceptibility effects, from which neuroimaging benefits the most. Optimal gradient performance is considered a pre-requisite to attain the full potential of ultrahigh field magnetic resonance imaging (MRI).
The benefits of using tailored gradient coils for human brain imaging have been well acknowledged. Unfortunately, conventional head-only gradient coils have two major technical limitations, including (a) a limited neck-shoulder clearance and (b) a limited cooling capacity.
Theoretical analyses suggest that, for a cylindrical gradient coil having a radius R, the gradient strength scales roughly 1/R, and the inductance scales about R5. Due to the fact that conventional MM scanners are designed to cover a large field of view, the gradient strength and the inductance of these coils are thus inherently limited by the physical size of the coil.
In addition, increasing the electrical current and voltage of a gradient amplifier output has been a major technical pursuit to enhance gradient performance. However, as the electrical current in the coil increases, the ohmic heating also becomes more pronounced. Thus, efficient cooling is needed for heat dissipation which is critical for the operation of the gradient coils.
Furthermore, the peripheral nerve stimulation (PNS) and the cardiac stimulation (CS) are two physiological factors that ultimately limit the performance of a gradient coil. PNS and CS thresholds are dB/dt related, where B is the magnetic field strength, which can be expressed as ∫γG(r)dr, where G is the gradient field along the coil length r. For a body gradient coil, G typically extends to a large distance r, and thus possesses a high risk to induce PNS and CS. It is thus suboptimal, for considerations, to employ a long whole-body gradient coil to image the brain.
To overcome the use of a long whole-body coil in brain imaging, a functional MRI technology has been developed in the form of a local gradient insert which enabled a fast imaging sequence, such as the echo planar imaging and the high resolution MM, to be implemented on clinical scanners. Nevertheless, despite MRI technology advancement, there are still two major technical issues associated with the conventional gradient insert design which include: a) the “shoulder clearance” issue and (b) cooling.
Regarding the “shoulder clearance”, in conventional cylindrical coil design, the coil has to reach a certain length in order to achieve a volume with high fidelity to the linear gradient field suitable for human brain imaging. However, since the inner diameter of the cylindrical coil does not provide clearance for the shoulders of a typical adult, one cannot place the center of the human brain at the center of the gradient coil where a uniform magnetic field is produced. As depicted in FIG. 1, the head of the human patient is displaced from the center of the gradient coil featuring the uniform region of the magnetic field. Due to this displacement, disadvantageously, only a fraction of the “sweet spot” (i.e., the uniform region) is used for neuroimaging.
Regarding the cooling issue, modern gradient amplifiers which are capable of providing a current value of 600 amperes, or more, are needed in the gradient coil and are readily available.
However, the high current used in the operation of this gradient coil generates a large amount of heat. For example, for a resistance of 0.5 ohm, with a current of 600 amperes and 60% duty cycle, the Ohmic heating Q may reach a level as high as 108 kW from a single gradient coil. Driving three gradient coils simultaneously (as in diffusion imaging) would triple the amount of heating. A relatively small coil size preferable for the head-only gradient coils exacerbates the heating problem due to reduction of the mass and the volume available for cooling tubes.
To mitigate the “shoulder clearance” problem, many previous approaches have relied on asymmetric head gradient designs. These designs are appealing because a) they may reduce the potential of PNS and CS since the shoulders and torso are disposed outside of the main gradient field; and b) a field linear volume is created at the end of the cylinder, and thus eliminates the “shoulder clearance” problem. However, the asymmetric head gradient also has several undesirable features, such as: in the asymmetric design, it is more difficult to balance the torque and to provide effective eddy current shielding, and, the linearity of the gradient field is much poorer than in conventional symmetric design. An additional shortcoming of the asymmetric design is, that due to the fact that Maxwell terms (concomitant terms) include odd orders, as well as even orders, their effect on the diffusion pulse sequence is undesirably complicated.
While some of these problems (such as the image distortions associated with gradient field nonlinearity might be manageable by applying reconstruction processing principles, in a diffusion MRI, b-factors associated with diffusion concomitant terms and their effect on fiber tracking might be less straightforward to quantify.
“Folded gradient” design is another approach to mitigate the “shoulder clearance” problem. In a conventional cylindrical transverse gradient coil design, the segments in the center of the coil (active segments) contribute to the desired magnetic field, while the segments on both ends of the coil (return paths) generate an undesirable field and contribute to the overall length of the coil.
To generate a magnetic field, an electrical current carrier must form a closed loop. In a gradient coil, half of the loop generates a desired magnetic field, while the other half (the return path) is necessary to complete the electrical loop, however, the return path generates an undesired field, and takes up space, thus increasing the length of the coil in a traditional design.
Shortening the length of the coil by folding the return paths toward the center of the coil produces a highly non-linear gradient, because the return paths and active segments are both moved toward the center of the coil, while the magnetic fields generated by them have opposite signs. It is quite a technical challenge to optimize the magnetic field in the target volume due to the physical constraints.
Notably, a conceptually similar, but more extreme approach had been developed in which the return paths were co-axial to the active segments along the radial direction, and thus did not contribute to the overall length of the coil.
A further optimization of a gradient field based on co-axial return paths called “sandwich” gradient coil design, has been used, where wire loops are embedded in circular planar disks. The active segments of each loop are placed close to the inner surface, while the return paths are placed close to the outer surface of the disk. The disks are then sandwiched together. Active segments surrounding the inner surface generate the desired field, while the return paths serve as a shielding.
Several desirable features arise from the “sandwich” design coil, such as shortening of the coil, elimination of the “shoulder clearance” problem, and reaching a highly uniform gradient field. However, the efficiency in this system is relatively lower than that in the conventional transverse gradient coil.
The gradient coils of magnetic resonance imaging are described in numerous publications and Patents. For example, U.S. Pat. No. 5,378,989 describes a magnetic field gradient apparatus for using a magnetic resonance imaging employing open magnets which allow access to a patient while the patient is being imaged. The magnetic field gradient apparatus employs two gradient coil assemblies and a gradient coil amplifier. Each gradient coil assembly has a gradient coil carrier with at least one gradient coil disposed on it. Each gradient coil carrier is comprised of a cylinder with a flange at one end. The gradient coil assemblies are positioned in the bore of each open magnet and spaced apart from each other allowing access to the patient, as shown in FIG. 2. This system overcomes the “shoulder clearance” problem by placing a patient between two gradient coil assemblies. However, this arrangement only applies to an “open magnet”, which is used in the “open MRI” systems with clinical applications in low magnetic field strength (typically <0.5 Tesla), but has never been applied in the high field MRI (1.5 Tesla and above), because it is extremely challenging to generate uniform high magnetic field with the open magnet. The gradient coil design presented in '989 Patent does not apply to the modern high field magnet systems which use a cylindrical design with a patient positioned inside the magnet.
Another gradient coil arrangement, described in the Patent Application Publication No. 2012/0032679, is configured for generating a magnetic imaging field in an imaging region provided in a bore. The gradient coil assemblies include three separate actively shielded gradient windings for generating orthogonal gradient shields. This constitutes a total of six individual layers, three of which are the so-called primary windings (positive electrical current) and three of the shield windings (negative electric current). A space between the primary and shield windings allows for a sufficient gradient shield to be created inside the imaging gradient and also houses the cooling pipes.
As the return current path, and consequently, any generated magnetic field, is located outside of the bore, the return current path does not contribute substantially in the gradient path, thereby resulting in significant improvement in the linearity of the transverse gradient fields. This in turn allows for a reduction in the length of the gradient coil assembly.
However, this system, using cooling pipes, is susceptible to shortcomings associated with indirect cooling and direct internal cooling, and this design is only suitable for whole body MM system.
With the modern high-power gradient amplifiers, ohmic heating is a serious concern in gradient coil technology. Conventional gradient coil thermal management can be classified into 3 categories: 1) natural convection on the external surface of the gradient coil assembly, ii) forced convection between the coolant inside a tube and an adjacent current-carrying element with insulation dielectric material in between (referred to herein as an “indirect external cooling”), and iii) forced convection with the coolant inside a current-carrying element (such as a copper tube) of the gradient coil assembly (called “direct internal cooling”).
The natural convection suffers from extremely low heat transfer coefficient, leading to limited thermal management capacity.
In the “direct internal cooling”, when a coolant flows inside a copper tubing, the heat generated inside the copper tubing due to Ohmic heating effects will be dissipated to temperature-controlled coolant. The amount of heat removal capability of the forced convection inside the copper tubing is determined by Newton's Cooling Law.Q=hAΔT  (Eq. 1)where Q is the cooling capacity, A is the total heat transfer area between the source of heat and the coolant, h is the convective heat transfer coefficient, and ΔT is the the temperature difference between the surface and the coolant. A higher convective heat transfer coefficient indicates a better heat removal capacity of the coolant (i.e., better thermal management capacity).
The nature of the coolant internal flow is determined by the Reynolds number. Based on Reynolds number, the flow can be either a laminar flow or a turbulent flow.
                    Re        =                              ρ            ⁢            U            ⁢            d            ⁢            i                    μ                                    (                  Eq          .                                          ⁢          2                )            where ρ is coolant density, U is the coolant velocity, di is a hydraulic diameter (internal diameter of the tube), and μ is the viscosity of the coolant.
For the ohmic heating effect, heat generated inside the copper tube is uniformly distributed, thus the entire copper tube can be treated as a uniform heat flux boundary condition. Therefore, the following constant heat flux boundary condition correlations are applicable.
                              N          ⁢                      u                          l              ⁢              a              ⁢              m                                      =                  4          ⁢          .36                                    (                  Eq          .                                          ⁢          3                )                                          Nu          turb                =                                            (                              f                /                8                            )                        ⁢                          (                              Re                -                1000                            )                        ⁢            Pr                                1            +                          12.7              ⁢                                                (                                      f                    /                    8                                    )                                0.5                            ⁢                              (                                                      Pr                                          2                      /                      3                                                        -                  1                                )                                                                        (                  Eq          .                                          ⁢          4                )                                h        =                              Nu            ·            k                                d            i                                              (                  Eq          .                                          ⁢          5                )            where, Nu is the Nusselt number (dimensionless), f is the friction factor between the coolant and boundaries, Pr is Prandtl number, which is material property of coolant, h is the convective heat transfer coefficient, k is the thermal conductivity of coolant, di is an effective hydraulic diameter (internal diameter) of the copper tubing.
                              T          o                =                              T            i                    +                                                    q                s                ″                            ⁢              π              ⁢                              d                i                            ⁢              L                                                      m                .                            ⁢                              c                p                                                                        (                  Eq          .                                          ⁢          6                )                                          T          s                =                              T            o                    +                                    q              s              ″                        h                                              (                  Eq          .                                          ⁢          7                )                                          q          s          ″                =                                            I              2                        ⁢                          R              elec                                            π            ⁢                          d              o                        ⁢            L                                              (                  Eq          .                                          ⁢          8                )            where, To is the coolant outlet temperature, Ti is coolant inlet temperature, qs″ is the heat flux boundary condition caused by the joule heating, I is the current flowing through the copper tubing, Relec is the electrical resistance of solid copper wire. d0 is the outer diameter of the copper tubing, L is tube total length, m is the mass flow rate, and cp is the heat capacity of the coolant.
The pressure drop of the coolant at various flow rate through copper tubing is also an important factor to be taken into consideration.
                              Δ          ⁢          P                =                                                            1                2                            ⁢              f              ⁢              ρ              ⁢                              U                2                            ⁢                              L                                  d                  i                                                                    1              ⁢              0              ⁢              0              ⁢              0                                *                      0            .            1                    ⁢          4          ⁢          5                                    (                  Eq          .                                          ⁢          9                )            
                              m          .                =                              1            4                    ⁢          π          ⁢                      d            i            2                    ⁢          U                                    (                  Eq          .                                          ⁢          10                )            
where f is friction factor, L is the total length, ρ is coolant density. The pressure is converted to the unit of pressure per square inches (PSI). {dot over (m)} is the flow rate inside the copper tubing.
It follows from Eq. 1 that a better cooling performance can be achieved by two approaches: i) enhancing heat transfer coefficient h; and ii) maximizing heat transfer area A. For the indirect cooling, the bottle neck of the effective thermal management is the high thermal resistance of insulating materials with low thermal conductivity between the coolant and the copper tubing. The insulating materials used to stabilize electric current carrying materials (e.g. copper wires of gradient coils), for example epoxy, have a thermal conductivity less than 2.5 W/mK. In contrast, copper has a thermal conductivity of about 380 W/mK. It thus appears that a direct cooling inside copper tubing is a preferred approach by eliminating insulating materials between the coolant and the copper tubing. However, a high pressure drop ΔP associated with the internal cooling approaches must be taken into account as well.
For the direct internal cooling, increasing the heat transfer area A by increasing tubing diameter is preferred in terms of heat dissipation from the copper tubing. However, a compact configuration of cooling using small diameter tubing is preferred for enhancing current density, and thus, for achieving a high gradient coil efficiency (referred to as the gradient field strength per unit current).
As a trade-off, the pressure drop ΔP associated with the coolant flow rate and the copper tubing dimensions has to be evaluated (Eq. 9) to achieve the required cooling efficiency (Eq. 2-Eq. 8).
Analytical calculations were performed with a copper tubing with 1.6 mm and the outer diameter (do) of 3.2 mm, respectively. The overall length L of the tube was 15 m per quadrant. When the copper tubing carries 200 Amp current, massive ohmic heating is generated inside the copper tubing (Eq. 8) therefore, the high flow rate of the dielectric coolant (for example, Duratherm 450 Oil) is vital to achieve a desired thermal performance. The flow rate is a trade-off between the thermal performance and the pressure drop. Thus, the flow rate can be systematically adjusted to identify the optimal point for both acceptable thermal performance and pressure drop. The nature of the coolant flow transits from the laminar to the turbulent flow regime at ˜0.2 gallon per minute (GPM), where the effective heat transfer coefficient is improved dramatically. As a result, the sharp enhancement in heat transfer coefficient of coolant, copper tube surface temperature at the outlet decreases dramatically at 0.2 GPM. The transition phase between the laminar and the turbulent flow regime provides moderate increment in the heat transfer coefficient from laminar flow. However, the pressure drop across the copper tube is proportional to a square of the coolant velocity. In such a case, it is extremely challenging to maintain low surface temperature using high flow rate while keeping the pressure drop in a reasonable range (less than 200 pounds per square inch (PSI)), because practically most materials (e.g. hoses and tubes) cannot withstand a high pressure.
None of the conventional Mill scanners has solved the “shoulder clearance” problem in a single magnet bore arrangement. In addition, none of the prior art gradient coils used in the Mill scanners has overcome the shortcomings of the traditional cooling systems based on coolant flowing in tubes for cooling the gradient coils.
It would be highly desirable to fundamentally solve these two technical problems of the conventional gradient coils to achieve a torque balance and strong uniform magnetic field at the brain location during imaging, while achieving high gradient efficiency. It would be also highly desirable to provide a new cooling method to eliminate limitations associated with the cooling approach using a copper tubing which is a somewhat sub-optimal solution for the gradient coil cooling.